Lucjan Jacak, Piotr Sitko, Konrad Wieczorek, and Arkadiusz Wójs

Abstract

The book presents the wide range of topics in two-dimensional physics of quantum Hall systems, especially fractional quantum Hall states. It starts with the fundamental problems of quantum statistics in two dimensions and the corresponding braid group formalism. The braid group formalism of anyons (previously known) is developed for composite fermions. The effective formalism used in many-body quantum Hall theories — the Chern–Simons theory is also presented. The Chern–Simons theory of anyons (particles obeying fractional statistics) and composite fermions (related to Hall systems) is given, i ... More

The book presents the wide range of topics in two-dimensional physics of quantum Hall systems, especially fractional quantum Hall states. It starts with the fundamental problems of quantum statistics in two dimensions and the corresponding braid group formalism. The braid group formalism of anyons (previously known) is developed for composite fermions. The effective formalism used in many-body quantum Hall theories — the Chern–Simons theory is also presented. The Chern–Simons theory of anyons (particles obeying fractional statistics) and composite fermions (related to Hall systems) is given, in detail. Numerical studies, which play the important role in quantum Hall analyses, are presented for spherical systems (Haldane sphere). The composite fermion theory is tested in numerical studies. The concept of the hierarchy of condensed states of composite fermion excitations is introduced (in analogy to the Haldane hierarchy). The hierarchies of odd-denominator states and even-denominator states are presented. The BCS paired Hall state is also discussed. An introduction to multi-component quantum Hall systems and spin quantum Hall systems is sketched.

End Matter

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